If it's a Germanic word that makes it unlikely to come via French, without it clearly being a French loanword. And very basic words are unlikely to be borrowed; it's mostly modern or learned words that tend to get borrowed. And of course, if the Luxembourgish form clearly differs from the German form, you can also be fairly sure it must be relatively old.

I just think it's not always so obvious once a word has been assimilated, especially words reborrowed from East Central German dialects. I still advise against it unless it comes with a sturdy West Central etymology.

Given that Frankish is either entirely unattested or perhaps hinted at only by a single ~24-character inscription of uncertain meaning, and that the status of modern Luxembourgish as a standard language separate from [other] varieties of West Central High German is disputed, and that whether or not older forms/predecessors of Luxembourgish can be distinguished from Old and Middle High German is even more disputed, the derivation of Luxembourgish in general from Frankish is uncertain and close to being circular logic. And Victar is correct in noting that the assimilation of loans makes it dangerous to make assumptions about specific words. With that said... I don't want to not list Luxembourgish at all, and if it's listed, it has to be listed somewhere... it's just a mess. (It's also odd to list Luxembourgish as Frankish while Kölsch is German. But I've been intending to bring up Kölsch et al. for discussion once Low German is sorted.)

Some linguists think Luxembourgish is derived from Frankish / Old Franconian, some (e.g. Robert Bruch) think Luxembourgish is Moselle Franconian. Some (e.g. Bruch) think Moselle Franconian is derived from Frankish, some (e.g. Bradley Allan Holtman) consider Moselle Franconian to be West Central High German. It's a mess.

Of course, some of our language categories (e.g. Finno-Ugric vs Uralic) don't follow modern linguistic notions, either, they're just categories of convenience, so I could live with Luxembourgish being under Frankish for convenience, especially with a paragraph at WT:ALB to explain the varying views of the actual linguistic situation.

I'm not sure what you're saying though. Why can't West Central High German be Frankish? I think Frankish is really more of a political term than a linguistic one. There is no definite sound change or other kind of border to mark the change from Frankish to, say, Alemannic. I believe that Frankish is more or less synonymous with what the Romans called w:Istvaeonic, or at least the northern half of it.